Thevenin's Theorem

 

 

Thevenin's Theorem-Sometimes it is desirable to find a particular branch current in a circuit as the rest branch is varied while all other resistances and voltage sources remain constant. For instance, in the circuit shown in Fig. 1.23, it may be desire to find the current through R_L, for five values of R_L, assuming that R₁. R₂. R₃ and E remain constant. In such situations, the *solution can be obtain readily by applying

Thevenin's theorem stated below:

Any two-terminal network containing a number of e.m.f. sources and resistances can be replace by an equivalent series circuit having a voltage source E₀, in series with a resistance R₀ where,

E₀ = open circuited voltage between the two terminals.

R₀ = the resistance between two terminals of the circuit obtained by looking "in" at the terminals with load removed and voltage sources replaced by their internal resistances, if any.

To understand the use of this theorem, consider the two terminal circuit shown in Fig. 1.23. The circuit enclosed in the dotted box can be replace by one voltage E₀, in series with resistance R₀ as shown in Fig. 1.24. The behavior at the terminals AB and A'B' is the same for the two circuits, independent of the values of R_L, connected across the terminals.

ACTIVE CIRCUIT (Fig. 1.23), THEVENIN'S EQUIVALENT CKT. Fig. 1.24

 

(i)Finding E_0:

 This is the voltage between terminals A and B of the circuit when load R_L, is removed. Fig. 125 shows the circuit with load removed. The voltage drop across R₂, is the desired voltage E₀

Current through R₂ =

[caption id="attachment_5361" align="alignnone" width="180"] Thevenin's Theorem[/caption]

 

(ii)Finding R_0:

This is the resistance between terminals A and B with load removed and e.m.f. reduced to zero (See Fig. 1.26).

 

Resistance between terminals A and B is

R₀=parallel combination of R₁, and R₂, in series with R₃,

 

=

Thus, the value of R₀ is determined. Once the values of E₀ and R₀, are determined, then current through the load resistance R_L, can be found out easily (Refer to Fig. 1.24).

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